(Nazarbayev University School of Science and Technology, 2016-05-20) Matayev, Chingis
Porous Medium Equation (PME) is one of the simplest types of of nonlinear evolution equation
of parabolic type. It emerges in the description of di erent natural phenomena, and its theory and
properties depart strongly from the heat equation, ut = u, its most famous relative. Hence the
interest of its study, both for the pure mathematician and the applied scientist (Vazquez, 2006).
The aim of this paper is to study the Porous Medium Equation in one dimension.